Chapter 9.1, Problem 9E

Solution

To calculate: The number of distinguishable 11-letter words that can be formed from the word MISSISSIPPI.

The resultant value is 34,650 words of 11-letters.

Given information:

The given word is “MISSISSIPPI” consisting eleven letters.

Formula used: If an n -set contains $n_1$ objects of first kind, $n_2$ objects of a second kind, and so on, with $n_1+n_2+\cdots +n_k=n$ , then the number of distinguishable permutations of the n -set is given by $\frac{n!}{n_1!n_2!\cdots n_k!}$ .

Calculation:

There are total 11 letters in the word “MISSISSIPPI”. There are 4 S’s, 4 I’s, and 2 P’s in this word.

The values are $n=11,n_1=4,n_2=4,\text{and}{n}_3=2$ 11,

Use the formula $\frac{n!}{n_1!n_2!\cdots n_k!}$ and substitute the values,

  $\frac{11!}{4!4!2!}$

Now expand the factorial,

  $\frac{11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4!}{4!4\cdot 3\cdot 2\cdot 1\cdot 2}=34,650$

Therefore, there are 34,650 ways in which the 11-letter words can be formed.